Fletcher was shot from the Libyan embassy as she oversaw an anti-Muammar Gaddafi protest in St James's Square, London, in 1984. The embassy was besieged by British police but the culprits were not surrendered.

Cameron announced the renewal of the investigation after meeting Abdurrahim el-Keib, Libya's interim prime minister, in London. Cameron said the visit by detectives to Tripoli would be a "really positive step forward".

Investigations into, and speculation about, the killing of Fletcher have continued since 1984. In 1999, Libya accepted responsibility and paid compensation to her family which preceded the resumption of diplomatic relations between Tripoli and London.

Detectives visited Libya and interviewed suspects on several occasions after 1999. It is understood that they have focused on two men who became senior figures in Gaddafi's regime but it is not clear if they survived the war that led to his overthrow.

Commander Richard Walton, head of the Metropolitan police's counter-terrorism command, said the news was significant. "We have never lost our resolve to solve this murder and achieve justice for Yvonne's family," he said.

Keib was appointed interim prime minister before elections later this year, but Libya remains divided with a weak central government.

The international criminal court ruled last month that Libya could not try Saif al-Islam Gaddafi, the son of the former leader, fairly and ordered that he be sent to The Hague.

Gaddafi is in the custody of a regional militia which has refused to release him to the Keib government.

Keib spent much of his life working abroad as an academic and businessman in the United States and UAE, and played no part in Gaddafi's administration.

He told Cameron: "The Fletcher case is a case that is close to my heart personally. I had friends who were demonstrating that day next to the embassy. It is a sad story. It is very unfortunate that it has anything to do with the Libyan people."

The Libyan prime minister's visit to Downing Street comes days after the death of Abdelbaset al-Megrahi, the only person convicted over the Lockerbie bombing in 1988. Police in the US and Britain remain keen to continue their investigation into the attack on Pan Am Flight 103, which exploded above the Scottish town.

Downing Street later revealed that Keib met Lord Advocate Frank Mulholland, the Scottish government's senior legal officer, during his visit to discuss the investigation into the bombing of the Pan Am flight. Cameron also raised the issue of Gadaffi's support for the IRA during his talks with the Libyan prime minister.